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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Chord of contact of tangent, Pole and Polar

  • question_answer
    The locus of the middle points of chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y-10=0\] which passes through the origin, is [Roorkee 1989]

    A)            \[{{x}^{2}}+{{y}^{2}}+x+3y=0\]                                  

    B)            \[{{x}^{2}}+{{y}^{2}}-x+3y=0\]

    C)            \[{{x}^{2}}+{{y}^{2}}+x-3y=0\]                                    

    D)            \[{{x}^{2}}+{{y}^{2}}-x-3y=0\]

    Correct Answer: D

    Solution :

               Let the midpoint of chord be (h, k), then its equation is \[T={{S}_{1}}\] i.e., \[{{(p-x)}^{2}}=4qy\] \[={{h}^{2}}+{{k}^{2}}-2h-6k-10\]                    Since it passes through the origin, therefore                    \[{{h}^{2}}+{{k}^{2}}-h-3k=0\] or locus is \[{{x}^{2}}+{{y}^{2}}-x-3y=0\].


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